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## Homework Statement

Consider a system comprising two extended bodies, which have masses M

_{1}and M

_{2}and centers of mass at

**R**

_{1}and

**R**

_{2}. Prove that the CM of the whole system is at

[M

_{1}

**R**

_{1}+M

_{2}

**R**

_{2}] / [M

_{1}+M

_{2}]

## Homework Equations

Definition of CM

## The Attempt at a Solution

First I looked at the numerator of the equation given in the problem. If I replace

**R**

_{1}with the definition then M

_{1}cancels. The same logic applies to the second term in the numerator. This leaves me with just the summation of all the mr terms for the particles comprising mass 1 and 2 then in the denominator I have the total mass of the system. So the equation given is now in the form of the definition? I feel like this is trivial, but the book has it marked as a harder problem. I feel like I'm missing something and it can't be done this easily. Is my method correct?